[character history]
In canon, Haruka appears only in the dream world, starting with Watanuki's dream of him exorcising yet another menacing spirit. Through a series of meetings, he takes on the role of someone who sheds light on Watanuki’s situation, hearing out his thoughts and giving him something to reflect on, whether it is the nature of meetings, the implications of cooking food, or his grandson’s quirks. The two of them become friends - in one scene Haruka asks Watanuki if “[there is] nothing interesting to talk about”, implying that their conversations go beyond the exchange of advice.
He also serves as a guardian of sorts. In two instances, Haruka saves Watanuki from dying: during their first encounter, and when he pulls Watanuki back from his dream while he was recovering from falling out the window. He remarks that this was because he looked his grandson’s age. There are also two times when he warns Watanuki before a disastrous event occurs - he advises the boy to bring one of his dream balloons in an attempt to keep him safe from an accident, and, as mentioned earlier, he appears to Watanuki moments before Kohane’s mother attacks.
There are two subtle hints that Haruka was preparing for the series of events that Watanuki and Shizuka would encounter even before the beginning of the series. The first one was the handwritten book Watanuki found in the Doumeki storeroom, containing the exact information they were looking for. The ofuda on its cover is definitely Haruka’s - we see the arrow-ofuda motif a few chapters later, where the book worm consumes four more ofuda with the arrow as their central image, and he uses a similar-looking arrow to exorcise the spirit that was bearing down on Watanuki when they first met.
In his most recent appearance, it’s implied that he and Ichihara Yuuko were friends even when he was still alive, and he knows, to some degree, the circumstances that led to recent canon events: he “[prays] that the ‘butterfly’s dream’ may be realized.” This is a significant chapter in the sense that it is a ‘hello’ and a ‘goodbye’ - it is the first time they were able to meet in a dream not unlike Watanuki’s, and yet it is also the last chapter before the beginning of the arc wherein Yuuko is finally able to tell Watanuki her wish. From this perspective, we can see how Haruka’s role in canon mirrors his own precognitive abilities and personality - his arrival foreshadows important events, and cautions us to reflect on the choices that the characters have made before seeing how their consequences unfold.
Historical Footnote
If we assume that Haruka was at least 50 or so when he died, we can speculate that he died around 1993, approximately the time when Doumeki was in 5th grade (holic begins 2003-ish) and was born in the 1950s or earlier. During his lifetime, he would have been a witness to Japan's rapid economic growth, the popularity of consumerism, political unrest, and Westernization that resulted from efforts to recover from WWII. Furthermore, there was a rapid decline in the believers of Shinto and Buddhism between the 50s and early 70s, followed by a trend in the next five years to follow certain customs for increasing luck (e.g., getting a charm for safe travel). [source]. These factors would also have influenced him to become more flexible in personality while still being able to uphold traditional beliefs, and might have added a sense of urgency in his work since the "old ways" are in danger of being forgotten.